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A Geometric Preferential Attachment Model of Networks II

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Algorithms and Models for the Web-Graph (WAW 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4863))

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Abstract

A detailed understanding of expansion in complex networks can greatly aid in the design and analysis of algorithms for a variety of important network tasks, including routing messages, ranking nodes, and compressing graphs. This has motivated several recent investigations of expansion properties in real-world graphs and also in random models of real-world graphs, like the preferential attachment graph. The results point to a gap between real-world observations and theoretical models. Some real-world graphs are expanders and others are not, but a graph generated by the preferential attachment model is an expander whp .

We study a random graph G n that combines certain aspects of geometric random graphs and preferential attachment graphs. This model yields a graph with power-law degree distribution where the expansion property depends on a tunable parameter of the model.

The vertices of G n are n sequentially generated points x 1,x 2,...,x n chosen uniformly at random from the unit sphere in . After generating x t , we randomly connect it to m points from those points in x 1,x 2,...,x t − 1 ....

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Authors and Affiliations

  1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA15213, U.S.A.

    Abraham D. Flaxman, Alan M. Frieze & Juan Vera

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  1. Abraham D. Flaxman
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  2. Alan M. Frieze
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  3. Juan Vera
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Anthony Bonato Fan R. K. Chung

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© 2007 Springer-Verlag Berlin Heidelberg

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Flaxman, A.D., Frieze, A.M., Vera, J. (2007). A Geometric Preferential Attachment Model of Networks II. In: Bonato, A., Chung, F.R.K. (eds) Algorithms and Models for the Web-Graph. WAW 2007. Lecture Notes in Computer Science, vol 4863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77004-6_4

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  • DOI: https://doi.org/10.1007/978-3-540-77004-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77003-9

  • Online ISBN: 978-3-540-77004-6

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